Known swivel bearings or swivel casters of the above type, e.g. as described in DE-PS No. 16 05 465 or the DE-GM No. 82 28 224, are manufactured by first inserting the swivel bearing plate with the two bearing rows with the anti-friction elements realized as balls, into the essentially cylindrical cup wall which on its one end is bent over inwards, and then welding or in rarer cases riveting the cup to a fastening plate at the bottom of the swivel bearing cup, or to a fastening plate which forms this bottom. Thereafter the swivel bearing cup is frequently subjected to surface finishing such as galvanizing or the like. Experience has shown that the final welding or riveting of the wall of the swivel bearing cup to the bottom of the cup leads not infrequently to an undesired warping of the material, and to a consequent excessive or insufficient bearing play between the swivel bearing cup and the swivel bearing plate. This in turn causes irregular running and rotational stiffness of the swivel bearing, and above all gives rise to irregular and therefore increased loading, with consequent decreased operating life of such swivel bearings. Similar deleterious effects are caused by other surface finishing steps for the swivel bearing cup, whether they include immersion or spraying, upon the running properties of the balls.